Critical temperature of a Bose gas in an optical lattice

TL;DR

This paper develops a mean-field theoretical framework to accurately predict the critical temperature of a Bose gas in an optical lattice, accounting for interactions, finite-size effects, and excited band occupation, with validation against numerical results.

Contribution

It introduces practical formulas for the critical temperature of a Bose gas in an optical lattice, including corrections for interactions and finite-size effects, validated by numerical comparisons.

Findings

Excellent agreement between theory and numerical calculations

Practical expressions for critical temperature including various corrections

Applicable over a wide range of parameters

Abstract

We present theory for the critical temperature of a Bose gas in a combined harmonic lattice potential based on a mean-field description of the system. We develop practical expressions for the ideal-gas critical temperature, and corrections due to interactions, the finite-size effect, and the occupation of excited bands. We compare our expressions to numerical calculations and find excellent agreement over a wide parameter regime.